Finite Group DatabasebetaFinite Group Databasebeta| order | 37610 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D3761⋊C5 |
| unambiguous semidirect product | (C3761⋊C5)⋊C2 |
| Fitting, socle, derived, Sylow | C3761 ⋊ C2×C5 |
| Hall | C3761⋊C5 ⋊ C2 |
| Hall | D3761 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3761 | C2×C5 |
| LCS | G ▷ C3761 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3761 |
Polycyclic presentation:
2,5,3761|c^a=c^3760,c^b=c^2744386 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37610, 1);